Exponential analysis task - applications, methods, problems

This review article presents the problem of exponential analysis, its applications, limitations and problems that are relevant despite its more than two hundred years of history. During this time, many methods for solving the problem have been developed, but the greatest popularity and efficiency are demonstrated by Prony-like methods: the Padé-Laplace method, Prony method and the matrix pencil method, which are the subject of research in this work. The purpose of the study: to present the current state of the problem of exponential analysis, its main problems and methods for solving them. The main problems of these methods are: the issue of determining the number of exponents, choosing the optimal signal sampling frequency and reducing computational costs. The article presents solutions to these problems.